We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism...

We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the two-dimensional low temperature Ising phases for which we prove a variational principle. Key-words : non-Gibbsian states, variational principle, projections, weakly Gibbsian measures.

We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences (xk) such that xkx2k = 0 for all k. We compute the Hausdorff and Minkowski dimensions of these sets and show that they are typically different. The proof proceeds via a variational principle for mult...

A variational principle which (1) accommodates a deforming signal without an explicit model, and (2) provides a confidence measure for its result, is suggested for signal flow calculations.

The formation of interparticle contacts and neck growth by grain boundary and surface di€usion during the sintering of rows of spherical particles is modeled. It is shown that rows of identical particles sinter into a metastable equilibrium con®guration whereas rows of particles with di€erent sizes evolve continuously by sintering followed by relatively slow coarsening. During coarsening, small...

A parametric version of the Borwein-Preiss smooth variational principle is presented, which states that under suitable assumptions on a given convex function depending on a parameter, the minimum point of a smooth convex perturbation of it depends continuously on the parameter. Some applications are given: existence of a Nash equilibrium and a solution of a variational inequality for a system o...

In this paper we study the variational principle for the Navier-Stokes equation described in [Gom05], and clarify the role of boundary conditions. We show that in certain special cases this variational principle gives rise to new models for fluid equations.

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis’ entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is amalgamated with Hopfield-like learning rules resulting in an unsupervised learning model. The update rules are formulated with the aid of q-deformed calculus. Num...

In fluid mechanics, two ways exist to specify the fields. The one most often used is the Eulerian description, in which the fields are considered as functions of the position in space, and time. The Lagrangian description, on the other hand, is based on the observation that many quantities specifying the fluid refer more fundamental ly to small identifiable pieces of matter, the "fluid particle...

We discuss a smooth variational principle for partially smooth viscosity subdiierentials and explore its applications in nonsmooth analysis. Short Title: Partially smooth variational principles.